+1 d
Median return +0.27%Completed observations: 19
- Middle 50%
- -0.15% … +0.91%
- Positive returns
- 58%
PAX Gold · Sigma Moves
Closed-period price moves, measured against their own history. One engine. Five markets. No forecasts.
Latest closed period
PAX Gold's latest move against its own history.
PAXG Exceptional
+6.71%
+4.68σ
2 times in 4 years
2 comparable moves / 1,613 observations
Small historical sample What happened afterwards
All history-qualified moves of at least 2.5σ. Results after the event are descriptive statistics, not trading instructions.
+7 d
Median return +0.62%Completed observations: 19
- Middle 50%
- -2.86% … +3.80%
- Positive returns
- 63%
+30 d
Median return +2.84%Completed observations: 19
- Middle 50%
- -0.23% … +4.06%
- Positive returns
- 74%
Every rare move, in context
Instrument: binance:spot:PAXGUSDT
| Date | σ | Move | Observed rarity | +1 d | +7 d | +30 d |
|---|---|---|---|---|---|---|
| 28 Jan 2026 | +4.68σ | +6.71% | 2 times in 4 years2 comparable moves / 1,613 observations | -1.12% | -9.21% | -4.53% |
| 22 Jan 2026 | +3.38σ | +3.75% | About once every 80 days20 comparable moves / 1,607 observations | +0.55% | +10.03% | +3.25% |
| 20 Jan 2026 | +2.71σ | +2.62% | About once every 35 days46 comparable moves / 1,605 observations | -0.14% | +8.04% | +3.97% |
| 29 Dec 2025 | -4.78σ | -4.07% | 1 times in 4 years1 comparable moves / 1,583 observations | -0.09% | +1.86% | +26.97% |
| 22 Dec 2025 | +3.80σ | +2.70% | About once every 175 days9 comparable moves / 1,576 observations | +1.03% | -2.69% | +7.03% |
| 21 Oct 2025 | -3.49σ | -6.09% | About once every 101 days15 comparable moves / 1,514 observations | -0.16% | -3.17% | -0.57% |
| 17 Oct 2025 | -3.06σ | -4.46% | About once every 52 days29 comparable moves / 1,510 observations | +0.09% | -3.03% | -3.49% |
| 16 Oct 2025 | +4.51σ | +4.68% | 2 times in 4 years2 comparable moves / 1,509 observations | -4.46% | -7.20% | -7.73% |
| 13 Oct 2025 | +3.29σ | +2.60% | About once every 72 days21 comparable moves / 1,506 observations | +0.85% | +5.37% | +0.88% |
| 29 Sep 2025 | +2.72σ | +1.90% | About once every 39 days38 comparable moves / 1,492 observations | +0.73% | +3.52% | +2.82% |
| 22 Sep 2025 | +2.56σ | +1.79% | About once every 32 days47 comparable moves / 1,485 observations | +0.44% | +2.39% | +8.89% |
| 1 Aug 2025 | +3.32σ | +2.15% | About once every 72 days20 comparable moves / 1,433 observations | -0.08% | +0.62% | +2.84% |
| 10 Apr 2025 | +2.75σ | +3.78% | About once every 37 days36 comparable moves / 1,320 observations | +1.52% | +4.07% | +3.45% |
| 9 Apr 2025 | +2.85σ | +3.27% | About once every 40 days33 comparable moves / 1,319 observations | +3.78% | +9.00% | +7.62% |
| 5 Feb 2025 | +3.52σ | +2.21% | About once every 97 days13 comparable moves / 1,256 observations | -1.34% | +0.31% | +0.38% |
| 25 Nov 2024 | -3.69σ | -3.66% | About once every 132 days9 comparable moves / 1,184 observations | +0.27% | +0.27% | +0.11% |
| 6 Nov 2024 | -5.62σ | -3.00% | Not previously observed in 3 years0 comparable moves / 1,165 observations | +2.03% | -3.43% | -1.02% |
| 1 Oct 2024 | +2.69σ | +1.59% | About once every 34 days33 comparable moves / 1,129 observations | -0.34% | -1.68% | +2.84% |
| 12 Sep 2024 | +3.06σ | +1.59% | About once every 48 days23 comparable moves / 1,110 observations | +0.98% | +1.45% | +4.15% |
The number has a method behind it
Sigma measures the size of a log return relative to volatility estimated before the period. Rarity is counted from actual historical standardized moves, not inferred from a normal distribution.
σt = ln(Ct / Ct−1) / vtvt ← t−1, t−2, …
Volatility adapts to the market regime with EWMA (λ = 0.94 for daily and weekly observations). Current-period returns are excluded. Each historical σ uses its own prior volatility.
Both directions count toward rarity. Reference history spans up to five years. A period with no prior exceedances is labelled unprecedented in the observed sample; it is never given an invented recurrence interval.
Stock observations use split-adjusted price returns, without dividend reinvestment. Commodities are explicitly labelled ETF price proxies; they do not represent spot commodity prices.
Questions behind the sigma
What does a 3σ move mean?
The period log return is three times the volatility estimated from earlier periods. Sigma is signed: negative for declines and positive for rises.
Why not calculate rarity from a normal distribution?
Market returns have heavy tails and changing volatility. We count actual past absolute sigma exceedances for the same instrument and period.
Does “once every 200 days” predict the next event?
No. It is the number of historical observed periods divided by comparable moves. Events can cluster and the market regime can change.
How much history is required?
At least three years of valid standardized observations, after a one-year volatility warm-up. This normally requires approximately four years of source history.
Are all instruments directly comparable?
The engine is shared, but each instrument has its own prices, calendar, volatility and reference sample. Commodity cards use explicitly labelled ETF proxies.
What happens on quiet days?
The page shows the largest covered standardized move, the complete rarity scale and recent records. Missing data is reported separately from market calm.
For information only. Historical observations are not investment advice and do not predict future moves. A rare move can be followed by another rare move.